4. Probability
Basic Concepts of Probability
2:01 minutesProblem 3.1.34
Textbook Question
Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.
34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.
Verified step by step guidance1
Step 1: Understand the problem. The spreadsheet generates a random number between 1 and 4000, inclusive. Event B is defined as generating a number less than 500. We need to determine the number of outcomes in Event B and decide if it is a simple event.
Step 2: Define the total sample space. The sample space consists of all possible outcomes, which are the integers from 1 to 4000. Therefore, the total number of outcomes in the sample space is 4000.
Step 3: Determine the number of outcomes in Event B. Event B includes all numbers less than 500. These numbers are the integers from 1 to 499. The number of outcomes in Event B is therefore 499.
Step 4: Define a simple event. A simple event is an event that consists of exactly one outcome. For example, generating the number 250 would be a simple event because it corresponds to a single outcome.
Step 5: Analyze whether Event B is a simple event. Since Event B consists of 499 outcomes (all numbers from 1 to 499), it is not a simple event. A simple event must have exactly one outcome, and Event B has multiple outcomes.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Event
A simple event is an outcome or a combination of outcomes that cannot be broken down into simpler components. In probability, it refers to a single outcome from a sample space. For example, rolling a die and getting a '3' is a simple event, as it represents one specific outcome.
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Sample Space
The sample space is the set of all possible outcomes of a random experiment. In the context of generating a number from 1 to 4000, the sample space consists of all integers from 1 to 4000. Understanding the sample space is crucial for determining the total number of outcomes for any event.
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Event
An event is a subset of the sample space that includes one or more outcomes. In this case, Event B, which is generating a number less than 500, includes all numbers from 1 to 499. An event can be simple (one outcome) or compound (multiple outcomes), and recognizing this distinction is key to analyzing probability.
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